Pandas Profiling Report

Dataset statistics

Number of variables	9
Number of observations	400
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	28.2 KiB
Average record size in memory	72.3 B

Variable types

NUM	8
BOOL	1

Warnings

Serial No. has unique values Unique

Reproduction

Analysis started	2020-12-29 23:07:58.993781
Analysis finished	2020-12-29 23:08:13.033951
Duration	14.04 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

Serial No.
Real number (ℝ_≥0)

UNIQUE

Distinct	400
Distinct (%)	100.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	200.5
Minimum	1
Maximum	400
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	1
5-th percentile	20.95
Q1	100.75
median	200.5
Q3	300.25
95-th percentile	380.05
Maximum	400
Range	399
Interquartile range (IQR)	199.5

Descriptive statistics

Standard deviation	115.6143013
Coefficient of variation (CV)	0.5766299317
Kurtosis	-1.2
Mean	200.5
Median Absolute Deviation (MAD)	100
Skewness	0
Sum	80200
Variance	13366.66667
Monotocity	Strictly increasing

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
400	1	0.2%
137	1	0.2%
127	1	0.2%
128	1	0.2%
129	1	0.2%
130	1	0.2%
131	1	0.2%
132	1	0.2%
133	1	0.2%
134	1	0.2%
Other values (390)	390	97.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.2%
2	1	0.2%
3	1	0.2%
4	1	0.2%
5	1	0.2%

Value	Count	Frequency (%)
400	1	0.2%
399	1	0.2%
398	1	0.2%
397	1	0.2%
396	1	0.2%

GRE Score
Real number (ℝ_≥0)

Distinct	49
Distinct (%)	12.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	316.8075
Minimum	290
Maximum	340
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	290
5-th percentile	298
Q1	308
median	317
Q3	325
95-th percentile	336
Maximum	340
Range	50
Interquartile range (IQR)	17

Descriptive statistics

Standard deviation	11.47364611
Coefficient of variation (CV)	0.03621645988
Kurtosis	-0.700489457
Mean	316.8075
Median Absolute Deviation (MAD)	8
Skewness	-0.06289345936
Sum	126723
Variance	131.6445551
Monotocity	Not monotonic

Histogram with fixed size bins (bins=49)

Value	Count	Frequency (%)
324	19	4.8%
312	19	4.8%
316	14	3.5%
322	14	3.5%
314	14	3.5%
321	13	3.2%
325	13	3.2%
311	12	3.0%
317	12	3.0%
320	12	3.0%
Other values (39)	258	64.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
290	2	0.5%
293	1	0.2%
294	2	0.5%
295	4	1.0%
296	5	1.2%

Value	Count	Frequency (%)
340	8	2.0%
339	3	0.8%
338	4	1.0%
337	1	0.2%
336	5	1.2%

TOEFL Score
Real number (ℝ_≥0)

Distinct	29
Distinct (%)	7.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	107.41
Minimum	92
Maximum	120
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	92
5-th percentile	98
Q1	103
median	107
Q3	112
95-th percentile	118
Maximum	120
Range	28
Interquartile range (IQR)	9

Descriptive statistics

Standard deviation	6.069513777
Coefficient of variation (CV)	0.05650790222
Kurtosis	-0.5787784114
Mean	107.41
Median Absolute Deviation (MAD)	4
Skewness	0.0572159137
Sum	42964
Variance	36.83899749
Monotocity	Not monotonic

Histogram with fixed size bins (bins=29)

Value	Count	Frequency (%)
110	37	9.2%
105	28	7.0%
107	26	6.5%
104	25	6.2%
106	24	6.0%
112	21	5.2%
100	19	4.8%
99	18	4.5%
111	17	4.2%
109	17	4.2%
Other values (19)	168	42.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
92	1	0.2%
93	2	0.5%
94	1	0.2%
95	2	0.5%
96	4	1.0%

Value	Count	Frequency (%)
120	8	2.0%
119	9	2.2%
118	9	2.2%
117	7	1.8%
116	11	2.8%

University Rating
Real number (ℝ_≥0)

Distinct	5
Distinct (%)	1.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.0875
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	2
median	3
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	2

Descriptive statistics

Standard deviation	1.14372813
Coefficient of variation (CV)	0.3704382607
Kurtosis	-0.7962869645
Mean	3.0875
Median Absolute Deviation (MAD)	1
Skewness	0.1712602774
Sum	1235
Variance	1.308114035
Monotocity	Not monotonic

Histogram with fixed size bins (bins=5)

Value	Count	Frequency (%)
3	133	33.2%
2	107	26.8%
4	74	18.5%
5	60	15.0%
1	26	6.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	26	6.5%
2	107	26.8%
3	133	33.2%
4	74	18.5%
5	60	15.0%

Value	Count	Frequency (%)
5	60	15.0%
4	74	18.5%
3	133	33.2%
2	107	26.8%
1	26	6.5%

SOP
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	2.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.4
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	1
5-th percentile	1.5
Q1	2.5
median	3.5
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	1.5

Descriptive statistics

Standard deviation	1.006868641
Coefficient of variation (CV)	0.2961378357
Kurtosis	-0.6756103428
Mean	3.4
Median Absolute Deviation (MAD)	0.5
Skewness	-0.2757611681
Sum	1360
Variance	1.013784461
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
3.5	70	17.5%
4	70	17.5%
3	64	16.0%
4.5	53	13.2%
2.5	47	11.8%
5	37	9.2%
2	33	8.2%
1.5	20	5.0%
1	6	1.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	6	1.5%
1.5	20	5.0%
2	33	8.2%
2.5	47	11.8%
3	64	16.0%

Value	Count	Frequency (%)
5	37	9.2%
4.5	53	13.2%
4	70	17.5%
3.5	70	17.5%
3	64	16.0%

LOR
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	2.2%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.4525
Minimum	1
Maximum	5
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	1
5-th percentile	2
Q1	3
median	3.5
Q3	4
95-th percentile	5
Maximum	5
Range	4
Interquartile range (IQR)	1

Descriptive statistics

Standard deviation	0.8984775483
Coefficient of variation (CV)	0.2602396954
Kurtosis	-0.6624841166
Mean	3.4525
Median Absolute Deviation (MAD)	0.5
Skewness	-0.1069914787
Sum	1381
Variance	0.8072619048
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
3	85	21.2%
4	77	19.2%
3.5	73	18.2%
4.5	45	11.2%
2.5	39	9.8%
2	38	9.5%
5	35	8.8%
1.5	7	1.8%
1	1	0.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.2%
1.5	7	1.8%
2	38	9.5%
2.5	39	9.8%
3	85	21.2%

Value	Count	Frequency (%)
5	35	8.8%
4.5	45	11.2%
4	77	19.2%
3.5	73	18.2%
3	85	21.2%

CGPA
Real number (ℝ_≥0)

Distinct	168
Distinct (%)	42.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	8.598925
Minimum	6.8
Maximum	9.92
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	6.8
5-th percentile	7.64
Q1	8.17
median	8.61
Q3	9.0625
95-th percentile	9.601
Maximum	9.92
Range	3.12
Interquartile range (IQR)	0.8925

Descriptive statistics

Standard deviation	0.5963170965
Coefficient of variation (CV)	0.06934786575
Kurtosis	-0.4584756257
Mean	8.598925
Median Absolute Deviation (MAD)	0.45
Skewness	-0.06599054378
Sum	3439.57
Variance	0.3555940796
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
8	9	2.2%
8.76	8	2.0%
8.56	7	1.8%
8.45	6	1.5%
8.64	6	1.5%
9.11	6	1.5%
8.2	5	1.2%
8.8	5	1.2%
8.54	5	1.2%
8.65	5	1.2%
Other values (158)	338	84.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
6.8	1	0.2%
7.2	1	0.2%
7.25	1	0.2%
7.28	1	0.2%
7.3	1	0.2%

Value	Count	Frequency (%)
9.92	1	0.2%
9.91	1	0.2%
9.87	1	0.2%
9.82	1	0.2%
9.8	3	0.8%

Research
Boolean

Distinct	2
Distinct (%)	0.5%
Missing	0
Missing (%)	0.0%
Memory size	3.1 KiB

1	219
0	181

Common Values
Chart

Value	Count	Frequency (%)
1	219	54.8%
0	181	45.2%

Chance of Admit
Real number (ℝ_≥0)

Distinct	60
Distinct (%)	15.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	0.72435
Minimum	0.34
Maximum	0.97
Zeros	0
Zeros (%)	0.0%
Memory size	3.1 KiB

Quantile statistics

Minimum	0.34
5-th percentile	0.46
Q1	0.64
median	0.73
Q3	0.83
95-th percentile	0.94
Maximum	0.97
Range	0.63
Interquartile range (IQR)	0.19

Descriptive statistics

Standard deviation	0.1426093302
Coefficient of variation (CV)	0.1968790366
Kurtosis	-0.3891259175
Mean	0.72435
Median Absolute Deviation (MAD)	0.09
Skewness	-0.3534480999
Sum	289.74
Variance	0.02033742105
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0.64	17	4.2%
0.71	16	4.0%
0.72	15	3.8%
0.73	13	3.2%
0.78	12	3.0%
0.76	12	3.0%
0.94	12	3.0%
0.79	12	3.0%
0.7	12	3.0%
0.74	11	2.8%
Other values (50)	268	67.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0.34	2	0.5%
0.36	2	0.5%
0.38	2	0.5%
0.39	1	0.2%
0.42	3	0.8%

Value	Count	Frequency (%)
0.97	4	1.0%
0.96	7	1.8%
0.95	4	1.0%
0.94	12	3.0%
0.93	9	2.2%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

First rows

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
0	1	337	118	4	4.5	4.5	9.65	1	0.92
1	2	324	107	4	4.0	4.5	8.87	1	0.76
2	3	316	104	3	3.0	3.5	8.00	1	0.72
3	4	322	110	3	3.5	2.5	8.67	1	0.80
4	5	314	103	2	2.0	3.0	8.21	0	0.65
5	6	330	115	5	4.5	3.0	9.34	1	0.90
6	7	321	109	3	3.0	4.0	8.20	1	0.75
7	8	308	101	2	3.0	4.0	7.90	0	0.68
8	9	302	102	1	2.0	1.5	8.00	0	0.50
9	10	323	108	3	3.5	3.0	8.60	0	0.45

Last rows

	Serial No.	GRE Score	TOEFL Score	University Rating	SOP	LOR	CGPA	Research	Chance of Admit
390	391	314	102	2	2.0	2.5	8.24	0	0.64
391	392	318	106	3	2.0	3.0	8.65	0	0.71
392	393	326	112	4	4.0	3.5	9.12	1	0.84
393	394	317	104	2	3.0	3.0	8.76	0	0.77
394	395	329	111	4	4.5	4.0	9.23	1	0.89
395	396	324	110	3	3.5	3.5	9.04	1	0.82
396	397	325	107	3	3.0	3.5	9.11	1	0.84
397	398	330	116	4	5.0	4.5	9.45	1	0.91
398	399	312	103	3	3.5	4.0	8.78	0	0.67
399	400	333	117	4	5.0	4.0	9.66	1	0.95

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows